Question: Solve for $x$ and $y$ using elimination. ${2x-2y = -6}$ ${-2x-5y = -43}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-7y = -49$ $\dfrac{-7y}{{-7}} = \dfrac{-49}{{-7}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {2x-2y = -6}\thinspace$ to find $x$ ${2x - 2}{(7)}{= -6}$ $2x-14 = -6$ $2x-14{+14} = -6{+14}$ $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ You can also plug ${y = 7}$ into $\thinspace {-2x-5y = -43}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(7)}{= -43}$ ${x = 4}$